Distributed Singular Value Decomposition Through Least Squares

Singular value decomposition (SVD) is an essential matrix factorization technique that decomposes a matrix into singular values and corresponding singular vectors that form orthonormal bases. SVD has wide-ranging applications from principal component analysis (PCA) to matrix completion and approximation. Methods for computing the SVD of a matrix are extensive and involve optimization algorithms with some theoretical guarantees, though many of these techniques are not scalable in nature. We show the efficacy of a distributed stochastic gradient descent algorithm by implementing parallelized alternating least squares and prove theoretical guarantees for its convergence and empirical results, which allow for the development of a simple framework for solving SVD in a correct, scalable, and easily optimizable manner.

Name thesis:degree_name

Master

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Zhao, Freddie

Advisor dc:contributor.advisor

• Shah, Devavrat

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/157145

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/157145